Most ignorant post of the century. Literally shameful.
You used incel as an insult, so it's an insult. You used it as a derogatory term.
Also, mental health issues does not equal mentally ill. We don't call trans people mentally ill, but we do recognise that gender dysphoria is a mental health issue. now if the behaviour of people who are willing to shoot up strangers sound mentally healthy to you, that's your opinion. Bringing up studies, or lack thereof, is not an argument, since it's been proven many times how fallible the academia system is (Sokal affair etc). If you have specific points from a study though, i'm happy to examine them.
Last, let me remind you that you are spreading hate too. We have correctional systems and facilities in our society, don't you think we should put them to use in cases we need to? If someone is wrong about something, shouldn't we show them a better way? How are we going to do this if instead of being the better people. we fall to their level and respond to their hate with hate?